Earth's rotation causes the cycle of. If Earth began to spin a little bit faster.

Answer: Rotation is the circular movement of something around a fixed axis.

When you say Earth's rotation, you may be talking about the spin rotation, which is the rotation of Earth around her own axis (the one that goes from north pole to south pole)

This rotation causes the difference between night and day, which is called the diurnal cycle.

In this case, if the Earth bgan to spin a little bit faster, the first change we can notice is that the periods of day and night will be shorter (as the Earth spins faster, there is less time that each side of the Earth faces against the sun for each cycle), and then the days will be shorter.

Now, there will be a inconmensurable amount of changes with a change of the spin velocity, but the change in the duration of the day is maybe the more related to the previous question.

Earth's rotation causes the cycle of daylight and darkness. If the Earth rotated a little bit faster then daylight would be shorter, night time would be shorter, and their sum would be shorter. Like for example 11 hours of daylight, 11 hours of Darkness, for a total length of day of 22 hours instead of 24.